LMFDB - Embedded newform 820.2.bq.a.49.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(49,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 10, 19])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bq (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$22$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			49.1
Character	$\chi$	$=$	820.49
Dual form			820.2.bq.a.569.1

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.28615 + 2.28615i) q^{3} +(-0.249857 + 2.22206i) q^{5} +(0.324162 - 2.04668i) q^{7} -7.45299i q^{9} +(3.82132 - 1.94706i) q^{11} +(-2.11039 + 0.334253i) q^{13} +(-4.50877 - 5.65119i) q^{15} +(5.32295 - 2.71218i) q^{17} +(1.28670 - 8.12389i) q^{19} +(3.93794 + 5.42011i) q^{21} +(0.847314 - 1.16623i) q^{23} +(-4.87514 - 1.11040i) q^{25} +(10.1802 + 10.1802i) q^{27} +(-4.73011 + 9.28337i) q^{29} +(1.47200 - 4.53036i) q^{31} +(-4.28485 + 13.1874i) q^{33} +(4.46686 + 1.23169i) q^{35} +(-3.88208 + 1.26136i) q^{37} +(4.06052 - 5.58883i) q^{39} +(-0.375244 - 6.39212i) q^{41} +(3.89132 + 2.82721i) q^{43} +(16.5610 + 1.86219i) q^{45} +(-0.929626 - 5.86942i) q^{47} +(2.57358 + 0.836207i) q^{49} +(-5.96863 + 18.3695i) q^{51} +(-3.38397 - 1.72422i) q^{53} +(3.37171 + 8.97771i) q^{55} +(15.6309 + 21.5140i) q^{57} +(11.0277 + 8.01213i) q^{59} +(-0.261551 - 0.359994i) q^{61} +(-15.2539 - 2.41598i) q^{63} +(-0.215435 - 4.77294i) q^{65} +(1.75412 - 3.44265i) q^{67} +(0.729086 + 4.60326i) q^{69} +(0.559555 - 0.285107i) q^{71} +4.27944 q^{73} +(13.6839 - 8.60678i) q^{75} +(-2.74628 - 8.45218i) q^{77} +(-4.31181 - 4.31181i) q^{79} -24.1881 q^{81} -11.9600i q^{83} +(4.69666 + 12.5056i) q^{85} +(-10.4094 - 32.0370i) q^{87} +(10.6487 + 1.68659i) q^{89} +4.42764i q^{91} +(6.99187 + 13.7223i) q^{93} +(17.7303 + 4.88894i) q^{95} +(-0.175861 + 0.345147i) q^{97} +(-14.5114 - 28.4803i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 4 q^{11} - 10 q^{15} - 4 q^{19} + 12 q^{25} + 8 q^{29} - 8 q^{31} - 6 q^{35} + 40 q^{39} + 28 q^{41} - 4 q^{45} + 20 q^{49} - 32 q^{51} - 50 q^{55} + 12 q^{59} + 40 q^{61} - 10 q^{65} - 28 q^{69}+ \cdots + 4 q^{99}+O(q^{100}) $ 176 * q + 4 * q^11 - 10 * q^15 - 4 * q^19 + 12 * q^25 + 8 * q^29 - 8 * q^31 - 6 * q^35 + 40 * q^39 + 28 * q^41 - 4 * q^45 + 20 * q^49 - 32 * q^51 - 50 * q^55 + 12 * q^59 + 40 * q^61 - 10 * q^65 - 28 * q^69 - 108 * q^71 + 52 * q^75 + 48 * q^79 - 328 * q^81 + 98 * q^85 - 16 * q^89 + 26 * q^95 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{19}{20}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−2.28615	+	2.28615i	−1.31991	+	1.31991i	−0.406069	+	0.913843i	$0.633101\pi$
$3$	−2.28615	+	2.28615i	−1.31991	+	1.31991i	−0.913843	+	0.406069i	$0.866899\pi$
$4$		0			0
$5$	−0.249857	+	2.22206i	−0.111740	+	0.993738i
$5$	−0.249857	+	2.22206i	−0.111740	+	0.993738i
$6$		0			0
$7$	0.324162	−	2.04668i	0.122522	−	0.773572i	−0.847543	−	0.530727i	$-0.821919\pi$
$7$	0.324162	−	2.04668i	0.122522	−	0.773572i	0.970065	−	0.242846i	$-0.0780809\pi$
$8$		0			0
$9$		−	7.45299i		−	2.48433i
$10$		0			0
$11$	3.82132	−	1.94706i	1.15217	−	0.587061i	0.229752	−	0.973249i	$-0.426209\pi$
$11$	3.82132	−	1.94706i	1.15217	−	0.587061i	0.922420	+	0.386189i	$0.126209\pi$
$12$		0			0
$13$	−2.11039	+	0.334253i	−0.585317	+	0.0927050i	−0.442068	−	0.896982i	$-0.645755\pi$
$13$	−2.11039	+	0.334253i	−0.585317	+	0.0927050i	−0.143249	+	0.989687i	$0.545755\pi$
$14$		0			0
$15$	−4.50877	−	5.65119i	−1.16416	−	1.45913i
$16$		0			0
$17$	5.32295	−	2.71218i	1.29101	−	0.657800i	0.332562	−	0.943081i	$-0.392087\pi$
$17$	5.32295	−	2.71218i	1.29101	−	0.657800i	0.958444	+	0.285281i	$0.0920870\pi$
$18$		0			0
$19$	1.28670	−	8.12389i	0.295189	−	1.86375i	−0.179727	−	0.983717i	$-0.557521\pi$
$19$	1.28670	−	8.12389i	0.295189	−	1.86375i	0.474915	−	0.880032i	$-0.342479\pi$
$20$		0			0
$21$	3.93794	+	5.42011i	0.859329	+	1.18276i
$22$		0			0
$23$	0.847314	−	1.16623i	0.176677	−	0.243175i	−0.711489	−	0.702697i	$-0.751979\pi$
$23$	0.847314	−	1.16623i	0.176677	−	0.243175i	0.888167	+	0.459521i	$0.151979\pi$
$24$		0			0
$25$	−4.87514	−	1.11040i	−0.975029	−	0.222080i
$26$		0			0
$27$	10.1802	+	10.1802i	1.95919	+	1.95919i
$28$		0			0
$29$	−4.73011	+	9.28337i	−0.878360	+	1.72388i	−0.213450	+	0.976954i	$0.568470\pi$
$29$	−4.73011	+	9.28337i	−0.878360	+	1.72388i	−0.664910	+	0.746924i	$0.731530\pi$
$30$		0			0
$31$	1.47200	−	4.53036i	0.264379	−	0.813676i	−0.727456	−	0.686154i	$-0.759298\pi$
$31$	1.47200	−	4.53036i	0.264379	−	0.813676i	0.991836	−	0.127522i	$-0.0407024\pi$
$32$		0			0
$33$	−4.28485	+	13.1874i	−0.745896	+	2.29563i
$34$		0			0
$35$	4.46686	+	1.23169i	0.755037	+	0.208193i
$36$		0			0
$37$	−3.88208	+	1.26136i	−0.638210	+	0.207367i	−0.610209	−	0.792241i	$-0.708914\pi$
$37$	−3.88208	+	1.26136i	−0.638210	+	0.207367i	−0.0280016	+	0.999608i	$0.508914\pi$
$38$		0			0
$39$	4.06052	−	5.58883i	0.650203	−	0.894928i
$40$		0			0
$41$	−0.375244	−	6.39212i	−0.0586033	−	0.998281i
$41$	−0.375244	−	6.39212i	−0.0586033	−	0.998281i
$42$		0			0
$43$	3.89132	+	2.82721i	0.593421	+	0.431146i	0.843538	−	0.537070i	$-0.180469\pi$
$43$	3.89132	+	2.82721i	0.593421	+	0.431146i	−0.250116	+	0.968216i	$0.580469\pi$
$44$		0			0
$45$	16.5610	+	1.86219i	2.46877	+	0.277598i
$46$		0			0
$47$	−0.929626	−	5.86942i	−0.135600	−	0.856144i	−0.957903	−	0.287093i	$-0.907311\pi$
$47$	−0.929626	−	5.86942i	−0.135600	−	0.856144i	0.822303	−	0.569050i	$-0.192689\pi$
$48$		0			0
$49$	2.57358	+	0.836207i	0.367654	+	0.119458i
$50$		0			0
$51$	−5.96863	+	18.3695i	−0.835775	+	2.57225i
$52$		0			0
$53$	−3.38397	−	1.72422i	−0.464824	−	0.236840i	0.205862	−	0.978581i	$-0.434000\pi$
$53$	−3.38397	−	1.72422i	−0.464824	−	0.236840i	−0.670686	+	0.741741i	$0.734000\pi$
$54$		0			0
$55$	3.37171	+	8.97771i	0.454641	+	1.21055i
$56$		0			0
$57$	15.6309	+	21.5140i	2.07036	+	2.84961i
$58$		0			0
$59$	11.0277	+	8.01213i	1.43569	+	1.04309i	0.988921	+	0.148441i	$0.0474254\pi$
$59$	11.0277	+	8.01213i	1.43569	+	1.04309i	0.446769	+	0.894649i	$0.352575\pi$
$60$		0			0
$61$	−0.261551	−	0.359994i	−0.0334881	−	0.0460924i	0.791945	−	0.610593i	$-0.209069\pi$
$61$	−0.261551	−	0.359994i	−0.0334881	−	0.0460924i	−0.825433	+	0.564500i	$0.809069\pi$
$62$		0			0
$63$	−15.2539	−	2.41598i	−1.92181	−	0.304385i
$64$		0			0
$65$	−0.215435	−	4.77294i	−0.0267214	−	0.592010i
$66$		0			0
$67$	1.75412	−	3.44265i	0.214299	−	0.420586i	−0.758685	−	0.651458i	$-0.774158\pi$
$67$	1.75412	−	3.44265i	0.214299	−	0.420586i	0.972984	+	0.230872i	$0.0741577\pi$
$68$		0			0
$69$	0.729086	+	4.60326i	0.0877716	+	0.554168i
$70$		0			0
$71$	0.559555	−	0.285107i	0.0664069	−	0.0338360i	−0.420472	−	0.907306i	$-0.638135\pi$
$71$	0.559555	−	0.285107i	0.0664069	−	0.0338360i	0.486879	+	0.873470i	$0.338135\pi$
$72$		0			0
$73$	4.27944			0.500870			0.250435	−	0.968133i	$-0.419426\pi$
$73$	4.27944			0.500870			0.250435	+	0.968133i	$0.419426\pi$
$74$		0			0
$75$	13.6839	−	8.60678i	1.58008	−	0.993826i
$76$		0			0
$77$	−2.74628	−	8.45218i	−0.312968	−	0.963216i
$78$		0			0
$79$	−4.31181	−	4.31181i	−0.485116	−	0.485116i	0.421645	−	0.906761i	$-0.361453\pi$
$79$	−4.31181	−	4.31181i	−0.485116	−	0.485116i	−0.906761	+	0.421645i	$0.861453\pi$
$80$		0			0
$81$	−24.1881			−2.68757
$82$		0			0
$83$		−	11.9600i		−	1.31278i	−0.754421	−	0.656391i	$-0.772082\pi$
$83$		−	11.9600i		−	1.31278i	0.754421	−	0.656391i	$-0.227918\pi$
$84$		0			0
$85$	4.69666	+	12.5056i	0.509424	+	1.35642i
$86$		0			0
$87$	−10.4094	−	32.0370i	−1.11601	−	3.43472i
$88$		0			0
$89$	10.6487	+	1.68659i	1.12876	+	0.178778i	0.692760	−	0.721168i	$-0.256394\pi$
$89$	10.6487	+	1.68659i	1.12876	+	0.178778i	0.436001	+	0.899946i	$0.356394\pi$
$90$		0			0
$91$			4.42764i			0.464143i
$92$		0			0
$93$	6.99187	+	13.7223i	0.725023	+	1.42294i
$94$		0			0
$95$	17.7303	+	4.88894i	1.81909	+	0.501595i
$96$		0			0
$97$	−0.175861	+	0.345147i	−0.0178560	+	0.0350444i	−0.899762	−	0.436381i	$-0.856260\pi$
$97$	−0.175861	+	0.345147i	−0.0178560	+	0.0350444i	0.881906	+	0.471425i	$0.156260\pi$
$98$		0			0
$99$	−14.5114	−	28.4803i	−1.45845	−	2.86238i
$100$		0			0
$101$	1.19131	−	7.52162i	0.118539	−	0.748429i	−0.854783	−	0.518986i	$-0.826310\pi$
$101$	1.19131	−	7.52162i	0.118539	−	0.748429i	0.973322	−	0.229443i	$-0.0736904\pi$
$102$		0			0
$103$	−10.3066	+	7.48817i	−1.01554	+	0.737831i	−0.965363	−	0.260909i	$-0.915978\pi$
$103$	−10.3066	+	7.48817i	−1.01554	+	0.737831i	−0.0501744	+	0.998740i	$0.515978\pi$
$104$		0			0
$105$	−13.0278	+	7.39610i	−1.27138	+	0.721786i
$106$		0			0
$107$	−7.05907	−	9.71597i	−0.682426	−	0.939278i	0.317534	−	0.948247i	$-0.397145\pi$
$107$	−7.05907	−	9.71597i	−0.682426	−	0.939278i	−0.999960	+	0.00896845i	$0.997145\pi$
$108$		0			0
$109$	5.28923	−	5.28923i	0.506616	−	0.506616i	−0.406870	−	0.913486i	$-0.633380\pi$
$109$	5.28923	−	5.28923i	0.506616	−	0.506616i	0.913486	+	0.406870i	$0.133380\pi$
$110$		0			0
$111$	5.99136	−	11.7587i	0.568675	−	1.11609i
$112$		0			0
$113$	−6.73154	−	2.18721i	−0.633250	−	0.205755i	−0.0252359	−	0.999682i	$-0.508034\pi$
$113$	−6.73154	−	2.18721i	−0.633250	−	0.205755i	−0.608014	+	0.793926i	$0.708034\pi$
$114$		0			0
$115$	2.37973	+	2.17418i	0.221911	+	0.202743i
$116$		0			0
$117$	2.49118	+	15.7287i	0.230310	+	1.45412i
$118$		0			0
$119$	−3.82546	−	11.7736i	−0.350680	−	1.07928i
$120$		0			0
$121$	4.34581	−	5.98149i	0.395074	−	0.543772i
$122$		0			0
$123$	15.4712	+	13.7555i	1.39499	+	1.24029i
$124$		0			0
$125$	3.68547	−	10.5554i	0.329638	−	0.944107i
$126$		0			0
$127$	−10.4507	+	3.39565i	−0.927353	+	0.301315i	−0.733480	−	0.679711i	$-0.762105\pi$
$127$	−10.4507	+	3.39565i	−0.927353	+	0.301315i	−0.193873	+	0.981027i	$0.562105\pi$
$128$		0			0
$129$	−15.3596	+	2.43272i	−1.35234	+	0.214189i
$130$		0			0
$131$	−0.330425	−	0.107362i	−0.0288694	−	0.00938023i	0.294547	−	0.955637i	$-0.404831\pi$
$131$	−0.330425	−	0.107362i	−0.0288694	−	0.00938023i	−0.323416	+	0.946257i	$0.604831\pi$
$132$		0			0
$133$	−16.2099	−	5.26692i	−1.40558	−	0.456700i
$134$		0			0
$135$	−25.1647	+	20.0775i	−2.16584	+	1.72800i
$136$		0			0
$137$	11.4665	+	11.4665i	0.979653	+	0.979653i	0.999797	−	0.0201438i	$-0.00641242\pi$
$137$	11.4665	+	11.4665i	0.979653	+	0.979653i	−0.0201438	+	0.999797i	$0.506412\pi$
$138$		0			0
$139$	7.42078	−	5.39151i	0.629422	−	0.457302i	−0.226778	−	0.973946i	$-0.572819\pi$
$139$	7.42078	−	5.39151i	0.629422	−	0.457302i	0.856200	+	0.516645i	$0.172819\pi$
$140$		0			0
$141$	15.5437	+	11.2931i	1.30901	+	0.951054i
$142$		0			0
$143$	−7.41366	+	5.38634i	−0.619962	+	0.450428i
$144$		0			0
$145$	−19.4464	−	12.8301i	−1.61493	−	1.06548i
$146$		0			0
$147$	−7.79529	+	3.97190i	−0.642945	+	0.327597i
$148$		0			0
$149$	7.68967	+	3.91808i	0.629962	+	0.320982i	0.739657	−	0.672984i	$-0.234988\pi$
$149$	7.68967	+	3.91808i	0.629962	+	0.320982i	−0.109695	+	0.993965i	$0.534988\pi$
$150$		0			0
$151$	2.82187	+	17.8166i	0.229641	+	1.44990i	0.785625	+	0.618702i	$0.212341\pi$
$151$	2.82187	+	17.8166i	0.229641	+	1.44990i	−0.555985	+	0.831193i	$0.687659\pi$
$152$		0			0
$153$	−20.2139	−	39.6719i	−1.63419	−	3.20729i
$154$		0			0
$155$	9.69895	+	4.40283i	0.779039	+	0.353644i
$156$		0			0
$157$	−2.13928	+	13.5069i	−0.170733	+	1.07797i	0.742295	+	0.670073i	$0.233737\pi$
$157$	−2.13928	+	13.5069i	−0.170733	+	1.07797i	−0.913029	+	0.407895i	$0.866263\pi$
$158$		0			0
$159$	11.6781	−	3.79445i	0.926135	−	0.300919i
$160$		0			0
$161$	−2.11223	−	2.11223i	−0.166467	−	0.166467i
$162$		0			0
$163$			4.95273i			0.387928i	0.981009	+	0.193964i	$0.0621345\pi$
$163$			4.95273i			0.387928i	−0.981009	+	0.193964i	$0.937866\pi$
$164$		0			0
$165$	−28.2327	−	12.8162i	−2.19791	−	0.997738i
$166$		0			0
$167$	12.2932	−	12.2932i	0.951276	−	0.951276i	−0.0475906	−	0.998867i	$-0.515154\pi$
$167$	12.2932	−	12.2932i	0.951276	−	0.951276i	0.998867	+	0.0475906i	$0.0151543\pi$
$168$		0			0
$169$	−8.02172	+	2.60641i	−0.617055	+	0.200493i
$170$		0			0
$171$	−60.5473	−	9.58975i	−4.63017	−	0.733347i
$172$		0			0
$173$	7.54325			0.573502			0.286751	−	0.958005i	$-0.407425\pi$
$173$	7.54325			0.573502			0.286751	+	0.958005i	$0.407425\pi$
$174$		0			0
$175$	−3.85297	+	9.61791i	−0.291257	+	0.727045i
$176$		0			0
$177$	−43.5281	+	6.89417i	−3.27177	+	0.518198i
$178$		0			0
$179$	−1.85822	−	0.946810i	−0.138890	−	0.0707679i	0.383165	−	0.923680i	$-0.374834\pi$
$179$	−1.85822	−	0.946810i	−0.138890	−	0.0707679i	−0.522054	+	0.852912i	$0.674834\pi$
$180$		0			0
$181$	3.86443	+	7.58437i	0.287241	+	0.563742i	0.988867	−	0.148804i	$-0.0475422\pi$
$181$	3.86443	+	7.58437i	0.287241	+	0.563742i	−0.701626	+	0.712545i	$0.747542\pi$
$182$		0			0
$183$	1.42095	+	0.225056i	0.105039	+	0.0166366i
$184$		0			0
$185$	−1.83287	−	8.94140i	−0.134755	−	0.657384i
$186$		0			0
$187$	15.0599	−	20.7282i	1.10129	−	1.51580i
$188$		0			0
$189$	24.1357	−	17.5356i	1.75561	−	1.27553i
$190$		0			0
$191$	1.71634	−	1.71634i	0.124190	−	0.124190i	−0.642280	−	0.766470i	$-0.722011\pi$
$191$	1.71634	−	1.71634i	0.124190	−	0.124190i	0.766470	+	0.642280i	$0.222011\pi$
$192$		0			0
$193$	−0.153502	−	0.0782131i	−0.0110493	−	0.00562990i	0.448457	−	0.893804i	$-0.351974\pi$
$193$	−0.153502	−	0.0782131i	−0.0110493	−	0.00562990i	−0.459506	+	0.888174i	$0.651974\pi$
$194$		0			0
$195$	11.4042	+	10.4191i	0.816670	+	0.746131i
$196$		0			0
$197$	6.03541	−	18.5751i	0.430005	−	1.32342i	−0.468114	−	0.883668i	$-0.655066\pi$
$197$	6.03541	−	18.5751i	0.430005	−	1.32342i	0.898119	−	0.439752i	$-0.144934\pi$
$198$		0			0
$199$	18.5272	−	2.93442i	1.31336	−	0.208015i	0.539828	−	0.841775i	$-0.318489\pi$
$199$	18.5272	−	2.93442i	1.31336	−	0.208015i	0.773530	+	0.633760i	$0.218489\pi$
$200$		0			0
$201$	3.86024	+	11.8806i	0.272280	+	0.837993i
$202$		0			0
$203$	17.4668	+	12.6903i	1.22593	+	0.890687i
$204$		0			0
$205$	14.2975	+	0.763301i	0.998578	+	0.0533112i
$206$		0			0
$207$	−8.69189	−	6.31503i	−0.604128	−	0.438925i
$208$		0			0
$209$	−10.9008	−	33.5493i	−0.754025	−	2.32065i
$210$		0			0
$211$	8.77210	−	1.38936i	0.603896	−	0.0956477i	0.153003	−	0.988226i	$-0.451106\pi$
$211$	8.77210	−	1.38936i	0.603896	−	0.0956477i	0.450893	+	0.892578i	$0.351106\pi$
$212$		0			0
$213$	−0.627429	+	1.93103i	−0.0429907	+	0.132312i
$214$		0			0
$215$	−7.25452	+	7.94037i	−0.494754	+	0.541529i
$216$		0			0
$217$	−8.79502	−	4.48129i	−0.597045	−	0.304210i
$218$		0			0
$219$	−9.78345	+	9.78345i	−0.661104	+	0.661104i
$220$		0			0
$221$	−10.3269	+	7.50297i	−0.694666	+	0.504704i
$222$		0			0
$223$	9.09212	−	12.5142i	0.608853	−	0.838015i	−0.387629	−	0.921815i	$-0.626706\pi$
$223$	9.09212	−	12.5142i	0.608853	−	0.838015i	0.996483	+	0.0838008i	$0.0267059\pi$
$224$		0			0
$225$	−8.27579	+	36.3344i	−0.551720	+	2.42229i
$226$		0			0
$227$	−24.5471	−	3.88788i	−1.62925	−	0.258048i	−0.726168	−	0.687517i	$-0.758701\pi$
$227$	−24.5471	−	3.88788i	−1.62925	−	0.258048i	−0.903081	+	0.429470i	$0.858701\pi$
$228$		0			0
$229$	3.45303	+	6.77694i	0.228182	+	0.447833i	0.976503	−	0.215504i	$-0.0691395\pi$
$229$	3.45303	+	6.77694i	0.228182	+	0.447833i	−0.748321	+	0.663337i	$0.769139\pi$
$230$		0			0
$231$	25.6014	+	13.0446i	1.68445	+	0.858269i
$232$		0			0
$233$	6.28901	−	0.996081i	0.412007	−	0.0652554i	0.0530092	−	0.998594i	$-0.483119\pi$
$233$	6.28901	−	0.996081i	0.412007	−	0.0652554i	0.358997	+	0.933339i	$0.383119\pi$
$234$		0			0
$235$	13.2745	−	0.599169i	0.865934	−	0.0390855i
$236$		0			0
$237$	19.7149			1.28062
$238$		0			0
$239$	−14.1850	−	2.24668i	−0.917551	−	0.145326i	−0.320241	−	0.947336i	$-0.603764\pi$
$239$	−14.1850	−	2.24668i	−0.917551	−	0.145326i	−0.597310	+	0.802011i	$0.703764\pi$
$240$		0			0
$241$	0.703202	−	0.228484i	0.0452972	−	0.0147180i	−0.286281	−	0.958146i	$-0.592419\pi$
$241$	0.703202	−	0.228484i	0.0452972	−	0.0147180i	0.331578	+	0.943428i	$0.392419\pi$
$242$		0			0
$243$	24.7571	−	24.7571i	1.58817	−	1.58817i
$244$		0			0
$245$	−2.50113	+	5.50973i	−0.159792	+	0.352004i
$246$		0			0
$247$			17.5746i			1.11825i
$248$		0			0
$249$	27.3424	+	27.3424i	1.73276	+	1.73276i
$250$		0			0
$251$	−20.5307	+	6.67083i	−1.29589	+	0.421059i	−0.874148	−	0.485659i	$-0.838580\pi$
$251$	−20.5307	+	6.67083i	−1.29589	+	0.421059i	−0.421737	+	0.906718i	$0.638580\pi$
$252$		0			0
$253$	0.967143	−	6.10630i	0.0608038	−	0.383900i
$254$		0			0
$255$	−39.3270	−	17.8524i	−2.46275	−	1.11796i
$256$		0			0
$257$	1.27592	+	2.50413i	0.0795894	+	0.156203i	0.927372	−	0.374142i	$-0.122063\pi$
$257$	1.27592	+	2.50413i	0.0795894	+	0.156203i	−0.847782	+	0.530345i	$0.822063\pi$
$258$		0			0
$259$	1.32319	+	8.35426i	0.0822187	+	0.519109i
$260$		0			0
$261$	69.1889	+	35.2535i	4.28268	+	2.18214i
$262$		0			0
$263$	20.6070	−	10.4998i	1.27068	−	0.647444i	0.317046	−	0.948410i	$-0.397309\pi$
$263$	20.6070	−	10.4998i	1.27068	−	0.647444i	0.953635	+	0.300966i	$0.0973089\pi$
$264$		0			0
$265$	4.67684	−	7.08860i	0.287296	−	0.435449i
$266$		0			0
$267$	−28.2004	+	20.4888i	−1.72584	+	1.25389i
$268$		0			0
$269$	−16.2615	−	11.8147i	−0.991483	−	0.720355i	−0.0312379	−	0.999512i	$-0.509945\pi$
$269$	−16.2615	−	11.8147i	−0.991483	−	0.720355i	−0.960245	+	0.279157i	$0.909945\pi$
$270$		0			0
$271$	−11.3919	+	8.27669i	−0.692008	+	0.502773i	−0.877319	−	0.479907i	$-0.840670\pi$
$271$	−11.3919	+	8.27669i	−0.692008	+	0.502773i	0.185312	+	0.982680i	$0.440670\pi$
$272$		0			0
$273$	−10.1223	−	10.1223i	−0.612628	−	0.612628i
$274$		0			0
$275$	−20.7915	+	5.24901i	−1.25377	+	0.316527i
$276$		0			0
$277$	−8.34196	−	2.71047i	−0.501220	−	0.162856i	0.0474857	−	0.998872i	$-0.484879\pi$
$277$	−8.34196	−	2.71047i	−0.501220	−	0.162856i	−0.548705	+	0.836016i	$0.684879\pi$
$278$		0			0
$279$	−33.7647	−	10.9708i	−2.02144	−	0.656806i
$280$		0			0
$281$	11.4189	−	1.80858i	0.681197	−	0.107891i	0.193760	−	0.981049i	$-0.437932\pi$
$281$	11.4189	−	1.80858i	0.681197	−	0.107891i	0.487437	+	0.873158i	$0.337932\pi$
$282$		0			0
$283$	15.6863	−	5.09678i	0.932453	−	0.302972i	0.196888	−	0.980426i	$-0.436917\pi$
$283$	15.6863	−	5.09678i	0.932453	−	0.302972i	0.735565	+	0.677454i	$0.236917\pi$
$284$		0			0
$285$	−51.7111	+	29.3574i	−3.06310	+	1.73898i
$286$		0			0
$287$	−13.2043	−	1.30408i	−0.779423	−	0.0769773i
$288$		0			0
$289$	10.9856	−	15.1203i	0.646209	−	0.889431i
$290$		0			0
$291$	−0.387013	−	1.19110i	−0.0226871	−	0.0698238i
$292$		0			0
$293$	1.09051	+	6.88523i	0.0637085	+	0.402239i	0.998849	+	0.0479627i	$0.0152729\pi$
$293$	1.09051	+	6.88523i	0.0637085	+	0.402239i	−0.935141	+	0.354277i	$0.884727\pi$
$294$		0			0
$295$	−20.5588	+	22.5025i	−1.19698	+	1.31014i
$296$		0			0
$297$	58.7234	+	19.0804i	3.40748	+	1.10716i
$298$		0			0
$299$	−1.39835	+	2.74441i	−0.0808685	+	0.158713i
$300$		0			0
$301$	7.04782	−	7.04782i	0.406229	−	0.406229i
$302$		0			0
$303$	14.4721	+	19.9191i	0.831398	+	1.14432i
$304$		0			0
$305$	0.865279	−	0.491235i	0.0495457	−	0.0281281i
$306$		0			0
$307$	7.90327	−	5.74207i	0.451064	−	0.327717i	−0.338952	−	0.940804i	$-0.610072\pi$
$307$	7.90327	−	5.74207i	0.451064	−	0.327717i	0.790016	+	0.613087i	$0.210072\pi$
$308$		0			0
$309$	6.44332	−	40.6815i	0.366548	−	2.31429i
$310$		0			0
$311$	0.329562	+	0.646803i	0.0186878	+	0.0366768i	0.900162	−	0.435556i	$-0.143448\pi$
$311$	0.329562	+	0.646803i	0.0186878	+	0.0366768i	−0.881474	+	0.472233i	$0.843448\pi$
$312$		0			0
$313$	5.23725	−	10.2787i	0.296027	−	0.580985i	−0.694309	−	0.719677i	$-0.744290\pi$
$313$	5.23725	−	10.2787i	0.296027	−	0.580985i	0.990336	+	0.138692i	$0.0442898\pi$
$314$		0			0
$315$	9.17976	−	33.2915i	0.517221	−	1.87576i
$316$		0			0
$317$	−0.0752101	−	0.147608i	−0.00422422	−	0.00829050i	0.888885	−	0.458131i	$-0.151481\pi$
$317$	−0.0752101	−	0.147608i	−0.00422422	−	0.00829050i	−0.893109	+	0.449840i	$0.851481\pi$
$318$		0			0
$319$			44.6845i			2.50185i
$320$		0			0
$321$	38.3503	+	6.07409i	2.14051	+	0.339023i
$322$		0			0
$323$	−15.1844	−	46.7328i	−0.844884	−	2.60028i
$324$		0			0
$325$	10.6596	+	0.713843i	0.591288	+	0.0395969i
$326$		0			0
$327$			24.1840i			1.33738i
$328$		0			0
$329$	−12.3142			−0.678903
$330$		0			0
$331$	1.91409	+	1.91409i	0.105208	+	0.105208i	0.757751	−	0.652543i	$-0.226298\pi$
$331$	1.91409	+	1.91409i	0.105208	+	0.105208i	−0.652543	+	0.757751i	$0.726298\pi$
$332$		0			0
$333$	9.40094	+	28.9331i	0.515168	+	1.58553i
$334$		0			0
$335$	7.21151	+	4.75793i	0.394007	+	0.259954i
$336$		0			0
$337$	−9.90226			−0.539411			−0.269705	−	0.962943i	$-0.586926\pi$
$337$	−9.90226			−0.539411			−0.269705	+	0.962943i	$0.586926\pi$
$338$		0			0
$339$	20.3896	−	10.3890i	1.10741	−	0.564255i
$340$		0			0
$341$	−3.19588	−	20.1780i	−0.173067	−	1.09270i
$342$		0			0
$343$	9.13099	−	17.9206i	0.493027	−	0.967620i
$344$		0			0
$345$	−10.4109	+	0.469916i	−0.560505	+	0.0252994i
$346$		0			0
$347$	14.8883	+	2.35808i	0.799246	+	0.126588i	0.542681	−	0.839939i	$-0.317409\pi$
$347$	14.8883	+	2.35808i	0.799246	+	0.126588i	0.256565	+	0.966527i	$0.417409\pi$
$348$		0			0
$349$	−7.53768	−	10.3747i	−0.403483	−	0.555346i	0.558131	−	0.829753i	$-0.311519\pi$
$349$	−7.53768	−	10.3747i	−0.403483	−	0.555346i	−0.961614	+	0.274406i	$0.911519\pi$
$350$		0			0
$351$	−24.8870	−	18.0815i	−1.32837	−	0.965118i
$352$		0			0
$353$	17.6980	+	24.3592i	0.941970	+	1.29651i	0.955003	+	0.296595i	$0.0958511\pi$
$353$	17.6980	+	24.3592i	0.941970	+	1.29651i	−0.0130338	+	0.999915i	$0.504149\pi$
$354$		0			0
$355$	0.493718	+	1.31460i	0.0262038	+	0.0697719i
$356$		0			0
$357$	35.6618	+	18.1706i	1.88742	+	0.961689i
$358$		0			0
$359$	−3.24920	+	10.0000i	−0.171486	+	0.527781i	−0.999456	−	0.0329927i	$-0.989496\pi$
$359$	−3.24920	+	10.0000i	−0.171486	+	0.527781i	0.827969	+	0.560774i	$0.189496\pi$
$360$		0			0
$361$	−46.2719	−	15.0347i	−2.43536	−	0.791298i
$362$		0			0
$363$	3.73942	+	23.6098i	0.196269	+	1.23919i
$364$		0			0
$365$	−1.06925	+	9.50918i	−0.0559670	+	0.497733i
$366$		0			0
$367$	−10.3492	−	7.51913i	−0.540223	−	0.392495i	0.283945	−	0.958841i	$-0.408357\pi$
$367$	−10.3492	−	7.51913i	−0.540223	−	0.392495i	−0.824168	+	0.566345i	$0.808357\pi$
$368$		0			0
$369$	−47.6404	+	2.79670i	−2.48006	+	0.145590i
$370$		0			0
$371$	−4.62588	+	6.36698i	−0.240164	+	0.330557i
$372$		0			0
$373$	15.6502	−	5.08504i	0.810334	−	0.263294i	0.125595	−	0.992082i	$-0.459916\pi$
$373$	15.6502	−	5.08504i	0.810334	−	0.263294i	0.684739	+	0.728788i	$0.259916\pi$
$374$		0			0
$375$	15.7058	+	32.5569i	0.811045	+	1.68123i
$376$		0			0
$377$	6.87938	−	21.1726i	0.354306	−	1.09044i
$378$		0			0
$379$	−5.46388	+	16.8161i	−0.280660	+	0.863784i	0.707006	+	0.707208i	$0.250046\pi$
$379$	−5.46388	+	16.8161i	−0.280660	+	0.863784i	−0.987666	+	0.156576i	$0.949954\pi$
$380$		0			0
$381$	16.1290	−	31.6550i	0.826314	−	1.62173i
$382$		0			0
$383$	1.51852	+	1.51852i	0.0775928	+	0.0775928i	0.744838	−	0.667245i	$-0.232527\pi$
$383$	1.51852	+	1.51852i	0.0775928	+	0.0775928i	−0.667245	+	0.744838i	$0.732527\pi$
$384$		0			0
$385$	19.4675	−	3.99057i	0.992154	−	0.203378i
$386$		0			0
$387$	21.0712	−	29.0020i	1.07111	−	1.47425i
$388$		0			0
$389$	7.59759	+	10.4572i	0.385213	+	0.530200i	0.956956	−	0.290232i	$-0.0937326\pi$
$389$	7.59759	+	10.4572i	0.385213	+	0.530200i	−0.571743	+	0.820433i	$0.693733\pi$
$390$		0			0
$391$	1.34719	−	8.50584i	0.0681305	−	0.430159i
$392$		0			0
$393$	1.00085	−	0.509957i	0.0504861	−	0.0257239i
$394$		0			0
$395$	10.6585	−	8.50378i	0.536285	−	0.427871i
$396$		0			0
$397$	−5.24472	+	0.830682i	−0.263225	+	0.0416907i	−0.286652	−	0.958035i	$-0.592542\pi$
$397$	−5.24472	+	0.830682i	−0.263225	+	0.0416907i	0.0234270	+	0.999726i	$0.492542\pi$
$398$		0			0
$399$	49.0993	−	25.0173i	2.45804	−	1.25243i
$400$		0			0
$401$			5.68028i			0.283660i	0.989891	+	0.141830i	$0.0452986\pi$
$401$			5.68028i			0.283660i	−0.989891	+	0.141830i	$0.954701\pi$
$402$		0			0
$403$	−1.59221	+	10.0528i	−0.0793137	+	0.500767i
$404$		0			0
$405$	6.04359	−	53.7476i	0.300308	−	2.67074i
$406$		0			0
$407$	−12.3787	+	12.3787i	−0.613590	+	0.613590i
$408$		0			0
$409$	9.40096			0.464848			0.232424	−	0.972615i	$-0.425334\pi$
$409$	9.40096			0.464848			0.232424	+	0.972615i	$0.425334\pi$
$410$		0			0
$411$	−52.4286			−2.58611
$412$		0			0
$413$	19.9730	−	19.9730i	0.982809	−	0.982809i
$414$		0			0
$415$	26.5759	+	2.98830i	1.30456	+	0.146690i
$416$		0			0
$417$	−4.63922	+	29.2909i	−0.227183	+	1.43438i
$418$		0			0
$419$		−	21.3260i		−	1.04184i	−0.853604	−	0.520922i	$-0.825588\pi$
$419$		−	21.3260i		−	1.04184i	0.853604	−	0.520922i	$-0.174412\pi$
$420$		0			0
$421$	−25.7075	+	13.0986i	−1.25291	+	0.638389i	−0.949289	−	0.314405i	$-0.898195\pi$
$421$	−25.7075	+	13.0986i	−1.25291	+	0.638389i	−0.303619	+	0.952793i	$0.598195\pi$
$422$		0			0
$423$	−43.7448	+	6.92849i	−2.12694	+	0.336875i
$424$		0			0
$425$	−28.9618	+	7.31167i	−1.40485	+	0.354668i
$426$		0			0
$427$	−0.821576	+	0.418614i	−0.0397589	+	0.0202582i
$428$		0			0
$429$	4.63477	−	29.2628i	0.223769	−	1.41282i
$430$		0			0
$431$	−3.34046	−	4.59775i	−0.160904	−	0.221466i	0.720951	−	0.692986i	$-0.243705\pi$
$431$	−3.34046	−	4.59775i	−0.160904	−	0.221466i	−0.881855	+	0.471520i	$0.843705\pi$
$432$		0			0
$433$	−6.71198	+	9.23825i	−0.322557	+	0.443962i	−0.939246	−	0.343245i	$-0.888474\pi$
$433$	−6.71198	+	9.23825i	−0.322557	+	0.443962i	0.616689	+	0.787207i	$0.288474\pi$
$434$		0			0
$435$	73.7891	−	15.1258i	3.53792	−	0.725225i
$436$		0			0
$437$	−8.38407	−	8.38407i	−0.401064	−	0.401064i
$438$		0			0
$439$	−13.6324	+	26.7550i	−0.650637	+	1.27695i	0.296168	+	0.955136i	$0.404291\pi$
$439$	−13.6324	+	26.7550i	−0.650637	+	1.27695i	−0.946804	+	0.321810i	$0.895709\pi$
$440$		0			0
$441$	6.23224	−	19.1809i	0.296773	−	0.913375i
$442$		0			0
$443$	−11.4356	+	35.1953i	−0.543324	+	1.67218i	0.181618	+	0.983369i	$0.441867\pi$
$443$	−11.4356	+	35.1953i	−0.543324	+	1.67218i	−0.724942	+	0.688810i	$0.758133\pi$
$444$		0			0
$445$	−6.40837	+	23.2407i	−0.303786	+	1.10172i
$446$		0			0
$447$	−26.5371	+	8.62242i	−1.25516	+	0.407827i
$448$		0			0
$449$	14.7522	−	20.3047i	0.696201	−	0.958238i	−0.303784	−	0.952741i	$-0.598250\pi$
$449$	14.7522	−	20.3047i	0.696201	−	0.958238i	0.999985	−	0.00549712i	$-0.00174980\pi$
$450$		0			0
$451$	−13.8798	−	23.6957i	−0.653573	−	1.11579i
$452$		0			0
$453$	−47.1827	−	34.2803i	−2.21684	−	1.61063i
$454$		0			0
$455$	−9.83851	−	1.10628i	−0.461236	−	0.0518632i
$456$		0			0
$457$	−1.04677	−	6.60904i	−0.0489658	−	0.309158i	−1.00000		7.21698e-5i	$-0.999977\pi$
$457$	−1.04677	−	6.60904i	−0.0489658	−	0.309158i	0.951034	−	0.309086i	$-0.100023\pi$
$458$		0			0
$459$	81.7995	+	26.5783i	3.81807	+	1.24057i
$460$		0			0
$461$	2.01555	−	6.20321i	0.0938734	−	0.288912i	−0.893085	−	0.449888i	$-0.851464\pi$
$461$	2.01555	−	6.20321i	0.0938734	−	0.288912i	0.986958	+	0.160975i	$0.0514640\pi$
$462$		0			0
$463$	33.2366	+	16.9349i	1.54464	+	0.787031i	0.998709	−	0.0508023i	$-0.0161778\pi$
$463$	33.2366	+	16.9349i	1.54464	+	0.787031i	0.545926	+	0.837833i	$0.316178\pi$
$464$		0			0
$465$	−32.2388	+	12.1078i	−1.49504	+	0.561484i
$466$		0			0
$467$	−10.0345	−	13.8112i	−0.464339	−	0.639108i	0.511062	−	0.859544i	$-0.329252\pi$
$467$	−10.0345	−	13.8112i	−0.464339	−	0.639108i	−0.975402	+	0.220435i	$0.929252\pi$
$468$		0			0
$469$	−6.47738	−	4.70609i	−0.299098	−	0.217307i
$470$		0			0
$471$	−25.9881	−	35.7696i	−1.19747	−	1.64818i
$472$		0			0
$473$	20.3747	+	3.22704i	0.936832	+	0.148380i
$474$		0			0
$475$	−15.2936	+	38.1764i	−0.701718	+	1.75165i
$476$		0			0
$477$	−12.8506	+	25.2207i	−0.588389	+	1.15478i
$478$		0			0
$479$	−1.89880	−	11.9886i	−0.0867585	−	0.547771i	−0.992334	−	0.123586i	$-0.960560\pi$
$479$	−1.89880	−	11.9886i	−0.0867585	−	0.547771i	0.905575	−	0.424185i	$-0.139440\pi$
$480$		0			0
$481$	7.77108	−	3.95957i	0.354331	−	0.180541i
$482$		0			0
$483$	9.65775			0.439443
$484$		0			0
$485$	−0.722998	−	0.477012i	−0.0328297	−	0.0216600i
$486$		0			0
$487$	5.27994	+	16.2500i	0.239257	+	0.736357i	0.996528	+	0.0832562i	$0.0265320\pi$
$487$	5.27994	+	16.2500i	0.239257	+	0.736357i	−0.757271	+	0.653100i	$0.773468\pi$
$488$		0			0
$489$	−11.3227	−	11.3227i	−0.512030	−	0.512030i
$490$		0			0
$491$	−27.5635			−1.24392			−0.621962	−	0.783047i	$-0.713664\pi$
$491$	−27.5635			−1.24392			−0.621962	+	0.783047i	$0.713664\pi$
$492$		0			0
$493$			62.2438i			2.80332i
$494$		0			0
$495$	66.9108	−	25.1293i	3.00742	−	1.12948i
$496$		0			0
$497$	−0.402137	−	1.23765i	−0.0180383	−	0.0555162i
$498$		0			0
$499$	2.15968	+	0.342059i	0.0966805	+	0.0153127i	0.204587	−	0.978848i	$-0.434415\pi$
$499$	2.15968	+	0.342059i	0.0966805	+	0.0153127i	−0.107907	+	0.994161i	$0.534415\pi$
$500$		0			0
$501$			56.2083i			2.51120i
$502$		0			0
$503$	1.42494	+	2.79661i	0.0635350	+	0.124694i	0.920590	−	0.390530i	$-0.127708\pi$
$503$	1.42494	+	2.79661i	0.0635350	+	0.124694i	−0.857055	+	0.515225i	$0.827708\pi$
$504$		0			0
$505$	16.4159	+	4.52649i	0.730496	+	0.201426i
$506$		0			0
$507$	12.3802	−	24.2975i	0.549825	−	1.07909i
$508$		0			0
$509$	11.3241	+	22.2248i	0.501933	+	0.985099i	0.993454	+	0.114233i	$0.0364411\pi$
$509$	11.3241	+	22.2248i	0.501933	+	0.985099i	−0.491521	+	0.870866i	$0.663559\pi$
$510$		0			0
$511$	1.38723	−	8.75863i	0.0613675	−	0.387459i
$512$		0			0
$513$	95.8019	−	69.6042i	4.22976	−	3.07310i
$514$		0			0
$515$	−14.0640	−	24.7729i	−0.619735	−	1.09162i
$516$		0			0
$517$	−14.9805	−	20.6189i	−0.658842	−	0.906819i
$518$		0			0
$519$	−17.2450	+	17.2450i	−0.756972	+	0.756972i
$520$		0			0
$521$	3.87796	−	7.61092i	0.169896	−	0.333441i	−0.790321	−	0.612692i	$-0.790086\pi$
$521$	3.87796	−	7.61092i	0.169896	−	0.333441i	0.960218	+	0.279252i	$0.0900864\pi$
$522$		0			0
$523$	−28.4767	−	9.25263i	−1.24520	−	0.404589i	−0.389000	−	0.921238i	$-0.627179\pi$
$523$	−28.4767	−	9.25263i	−1.24520	−	0.404589i	−0.856198	+	0.516649i	$0.827179\pi$
$524$		0			0
$525$	−13.1795	−	30.7965i	−0.575202	−	1.34407i
$526$		0			0
$527$	−4.45174	−	28.1072i	−0.193921	−	1.22437i
$528$		0			0
$529$	6.46525	+	19.8980i	0.281098	+	0.865129i
$530$		0			0
$531$	59.7143	−	82.1897i	2.59138	−	3.56673i
$532$		0			0
$533$	2.92850	+	13.3644i	0.126847	+	0.578878i
$534$		0			0
$535$	23.3533	−	13.2581i	1.00965	−	0.573197i
$536$		0			0
$537$	6.41273	−	2.08362i	0.276730	−	0.0899149i
$538$		0			0
$539$	11.4626	−	1.81550i	0.493730	−	0.0781991i
$540$		0			0
$541$	−37.6147	−	12.2218i	−1.61718	−	0.525455i	−0.645909	−	0.763415i	$-0.723521\pi$
$541$	−37.6147	−	12.2218i	−1.61718	−	0.525455i	−0.971275	+	0.237960i	$0.923521\pi$
$542$		0			0
$543$	−26.1737	−	8.50435i	−1.12322	−	0.364957i
$544$		0			0
$545$	10.4314	+	13.0746i	0.446834	+	0.560052i
$546$		0			0
$547$	−0.344193	−	0.344193i	−0.0147166	−	0.0147166i	0.699710	−	0.714427i	$-0.253312\pi$
$547$	−0.344193	−	0.344193i	−0.0147166	−	0.0147166i	−0.714427	+	0.699710i	$0.753312\pi$
$548$		0			0
$549$	−2.68303	+	1.94934i	−0.114509	+	0.0831956i
$550$		0			0
$551$	69.3308	+	50.3718i	2.95359	+	2.14591i
$552$		0			0
$553$	−10.2226	+	7.42716i	−0.434710	+	0.315835i
$554$		0			0
$555$	24.6316	+	16.2512i	1.04555	+	0.689824i
$556$		0			0
$557$	25.6426	−	13.0656i	1.08651	−	0.553606i	0.183412	−	0.983036i	$-0.441286\pi$
$557$	25.6426	−	13.0656i	1.08651	−	0.553606i	0.903100	+	0.429430i	$0.141286\pi$
$558$		0			0
$559$	−9.15721	−	4.66583i	−0.387309	−	0.197344i
$560$		0			0
$561$	12.9586	+	81.8172i	0.547111	+	3.45433i
$562$		0			0
$563$	11.0703	+	21.7267i	0.466558	+	0.915672i	0.997660	+	0.0683646i	$0.0217781\pi$
$563$	11.0703	+	21.7267i	0.466558	+	0.915672i	−0.531102	+	0.847308i	$0.678222\pi$
$564$		0			0
$565$	6.54205	−	14.4114i	0.275226	−	0.606293i
$566$		0			0
$567$	−7.84088	+	49.5054i	−0.329286	+	2.07903i
$568$		0			0
$569$	−29.4612	+	9.57252i	−1.23508	+	0.401301i	−0.852551	−	0.522644i	$-0.824946\pi$
$569$	−29.4612	+	9.57252i	−1.23508	+	0.401301i	−0.382526	+	0.923945i	$0.624946\pi$
$570$		0			0
$571$	9.85372	+	9.85372i	0.412365	+	0.412365i	0.882562	−	0.470196i	$-0.155817\pi$
$571$	9.85372	+	9.85372i	0.412365	+	0.412365i	−0.470196	+	0.882562i	$0.655817\pi$
$572$		0			0
$573$			7.84761i			0.327839i
$574$		0			0
$575$	−5.42575	+	4.74467i	−0.226270	+	0.197866i
$576$		0			0
$577$	−11.4980	+	11.4980i	−0.478670	+	0.478670i	−0.904706	−	0.426036i	$-0.859910\pi$
$577$	−11.4980	+	11.4980i	−0.478670	+	0.478670i	0.426036	+	0.904706i	$0.359910\pi$
$578$		0			0
$579$	0.529736	−	0.172122i	0.0220151	−	0.00715313i
$580$		0			0
$581$	−24.4783	−	3.87698i	−1.01553	−	0.160844i
$582$		0			0
$583$	−16.2884			−0.674597
$584$		0			0
$585$	−35.5727	+	1.60564i	−1.47075	+	0.0663849i
$586$		0			0
$587$	33.5144	−	5.30816i	1.38329	−	0.219091i	0.579967	−	0.814640i	$-0.303065\pi$
$587$	33.5144	−	5.30816i	1.38329	−	0.219091i	0.803319	+	0.595549i	$0.203065\pi$
$588$		0			0
$589$	−34.9101	−	17.7876i	−1.43845	−	0.732924i
$590$		0			0
$591$	28.6676	+	56.2634i	1.17923	+	2.31437i
$592$		0			0
$593$	−15.7642	−	2.49680i	−0.647358	−	0.102531i	−0.175883	−	0.984411i	$-0.556278\pi$
$593$	−15.7642	−	2.49680i	−0.647358	−	0.102531i	−0.471475	+	0.881880i	$0.656278\pi$
$594$		0			0
$595$	27.1174	−	5.55872i	1.11171	−	0.227885i
$596$		0			0
$597$	−35.6475	+	49.0645i	−1.45895	+	2.00808i
$598$		0			0
$599$	−9.24557	+	6.71730i	−0.377764	+	0.274461i	−0.760423	−	0.649428i	$-0.775008\pi$
$599$	−9.24557	+	6.71730i	−0.377764	+	0.274461i	0.382659	+	0.923890i	$0.375008\pi$
$600$		0			0
$601$	2.48030	−	2.48030i	0.101174	−	0.101174i	−0.654708	−	0.755882i	$-0.727208\pi$
$601$	2.48030	−	2.48030i	0.101174	−	0.101174i	0.755882	+	0.654708i	$0.227208\pi$
$602$		0			0
$603$	−25.6580	−	13.0734i	−1.04488	−	0.532391i
$604$		0			0
$605$	12.2054	+	11.1512i	0.496221	+	0.453360i
$606$		0			0
$607$	7.94215	−	24.4434i	0.322362	−	0.992129i	−0.650255	−	0.759716i	$-0.725338\pi$
$607$	7.94215	−	24.4434i	0.322362	−	0.992129i	0.972617	−	0.232413i	$-0.0746620\pi$
$608$		0			0
$609$	−68.9437	+	10.9196i	−2.79374	+	0.442485i
$610$		0			0
$611$	3.92374	+	12.0760i	0.158738	+	0.488544i
$612$		0			0
$613$	−23.4739	−	17.0548i	−0.948101	−	0.688836i	0.00225583	−	0.999997i	$-0.499282\pi$
$613$	−23.4739	−	17.0548i	−0.948101	−	0.688836i	−0.950357	+	0.311162i	$0.899282\pi$
$614$		0			0
$615$	−34.4312	+	30.9412i	−1.38840	+	1.24767i
$616$		0			0
$617$	−13.8249	−	10.0444i	−0.556571	−	0.404372i	0.273632	−	0.961835i	$-0.411775\pi$
$617$	−13.8249	−	10.0444i	−0.556571	−	0.404372i	−0.830202	+	0.557462i	$0.811775\pi$
$618$		0			0
$619$	3.05607	+	9.40561i	0.122834	+	0.378043i	0.993500	−	0.113831i	$-0.0363121\pi$
$619$	3.05607	+	9.40561i	0.122834	+	0.378043i	−0.870666	+	0.491874i	$0.836312\pi$
$620$		0			0
$621$	20.4983	−	3.24661i	0.822569	−	0.130282i
$622$		0			0
$623$	6.90382	−	21.2478i	0.276596	−	0.851274i
$624$		0			0
$625$	22.5340	+	10.8267i	0.901361	+	0.433068i
$626$		0			0
$627$	101.620	+	51.7778i	4.05830	+	2.06781i
$628$		0			0
$629$	−17.2431	+	17.2431i	−0.687527	+	0.687527i
$630$		0			0
$631$	−20.8117	+	15.1206i	−0.828500	+	0.601940i	−0.919135	−	0.393944i	$-0.871110\pi$
$631$	−20.8117	+	15.1206i	−0.828500	+	0.601940i	0.0906346	+	0.995884i	$0.471110\pi$
$632$		0			0
$633$	−16.8781	+	23.2307i	−0.670843	+	0.923336i
$634$		0			0
$635$	−4.93416	−	24.0706i	−0.195806	−	0.955214i
$636$		0			0
$637$	−5.71076	−	0.904495i	−0.226268	−	0.0358374i
$638$		0			0
$639$	−2.12490	−	4.17036i	−0.0840599	−	0.164977i
$640$		0			0
$641$	10.3734	+	5.28550i	0.409724	+	0.208765i	0.646690	−	0.762753i	$-0.276153\pi$
$641$	10.3734	+	5.28550i	0.409724	+	0.208765i	−0.236966	+	0.971518i	$0.576153\pi$
$642$		0			0
$643$	−34.5471	+	5.47172i	−1.36240	+	0.215783i	−0.794476	−	0.607296i	$-0.792254\pi$
$643$	−34.5471	+	5.47172i	−1.36240	+	0.215783i	−0.567927	+	0.823079i	$0.692254\pi$
$644$		0			0
$645$	−1.56796	−	34.7379i	−0.0617382	−	1.36780i
$646$		0			0
$647$	2.94741			0.115875			0.0579374	−	0.998320i	$-0.481548\pi$
$647$	2.94741			0.115875			0.0579374	+	0.998320i	$0.481548\pi$
$648$		0			0
$649$	57.7406	+	9.14522i	2.26652	+	0.358981i
$650$		0			0
$651$	30.3517	−	9.86186i	1.18958	−	0.386517i
$652$		0			0
$653$	−32.6248	+	32.6248i	−1.27671	+	1.27671i	−0.334205	+	0.942500i	$0.608468\pi$
$653$	−32.6248	+	32.6248i	−1.27671	+	1.27671i	−0.942500	+	0.334205i	$0.891532\pi$
$654$		0			0
$655$	0.321124	−	0.707401i	0.0125473	−	0.0276404i
$656$		0			0
$657$		−	31.8946i		−	1.24433i
$658$		0			0
$659$	4.18301	+	4.18301i	0.162947	+	0.162947i	0.783871	−	0.620924i	$-0.213242\pi$
$659$	4.18301	+	4.18301i	0.162947	+	0.162947i	−0.620924	+	0.783871i	$0.713242\pi$
$660$		0			0
$661$	−16.4610	+	5.34850i	−0.640259	+	0.208033i	−0.611114	−	0.791543i	$-0.709278\pi$
$661$	−16.4610	+	5.34850i	−0.640259	+	0.208033i	−0.0291447	+	0.999575i	$0.509278\pi$
$662$		0			0
$663$	6.45605	−	40.7619i	0.250732	−	1.58306i
$664$		0			0
$665$	15.7536	−	34.7035i	0.610898	−	1.34574i
$666$		0			0
$667$	6.81863	+	13.3823i	0.264018	+	0.518165i
$668$		0			0
$669$	7.82347	+	49.3954i	0.302473	+	1.90974i
$670$		0			0
$671$	−1.70040	−	0.866396i	−0.0656431	−	0.0334468i
$672$		0			0
$673$	−25.9857	+	13.2404i	−1.00168	+	0.510380i	−0.876319	−	0.481732i	$-0.840008\pi$
$673$	−25.9857	+	13.2404i	−1.00168	+	0.510380i	−0.125358	+	0.992112i	$0.540008\pi$
$674$		0			0
$675$	−38.3260	−	60.9342i	−1.47517	−	2.34536i
$676$		0			0
$677$	36.4115	−	26.4545i	1.39941	−	1.01673i	0.404651	−	0.914471i	$-0.367393\pi$
$677$	36.4115	−	26.4545i	1.39941	−	1.01673i	0.994758	−	0.102259i	$-0.0326071\pi$
$678$		0			0
$679$	0.649398	+	0.471815i	0.0249216	+	0.0181066i
$680$		0			0
$681$	65.0068	−	47.2302i	2.49106	−	1.80986i
$682$		0			0
$683$	19.2696	+	19.2696i	0.737332	+	0.737332i	0.972061	−	0.234729i	$-0.0754202\pi$
$683$	19.2696	+	19.2696i	0.737332	+	0.737332i	−0.234729	+	0.972061i	$0.575420\pi$
$684$		0			0
$685$	−28.3444	+	22.6144i	−1.08298	+	0.864052i
$686$		0			0
$687$	−23.3873	−	7.59899i	−0.892280	−	0.289919i
$688$		0			0
$689$	7.71782	+	2.50767i	0.294026	+	0.0955347i
$690$		0			0
$691$	−16.0294	+	2.53880i	−0.609786	+	0.0965807i	−0.453688	−	0.891161i	$-0.649892\pi$
$691$	−16.0294	+	2.53880i	−0.609786	+	0.0965807i	−0.156099	+	0.987741i	$0.549892\pi$
$692$		0			0
$693$	−62.9941	+	20.4680i	−2.39295	+	0.777516i
$694$		0			0
$695$	10.1261	+	17.8366i	0.384107	+	0.676579i
$696$		0			0
$697$	−19.3340	−	33.0072i	−0.732327	−	1.25024i
$698$		0			0
$699$	−12.1004	+	16.6548i	−0.457681	+	0.629943i
$700$		0			0
$701$	−6.36687	−	19.5952i	−0.240473	−	0.740101i	−0.996348	−	0.0853847i	$-0.972788\pi$
$701$	−6.36687	−	19.5952i	−0.240473	−	0.740101i	0.755875	−	0.654716i	$-0.227212\pi$
$702$		0			0
$703$	5.25212	+	33.1606i	0.198088	+	1.25068i
$704$		0			0
$705$	−28.9778	+	31.7174i	−1.09137	+	1.19455i
$706$		0			0
$707$	−15.0082	−	4.87645i	−0.564440	−	0.183398i
$708$		0			0
$709$	1.98073	−	3.88740i	0.0743878	−	0.145994i	−0.850817	−	0.525462i	$-0.823893\pi$
$709$	1.98073	−	3.88740i	0.0743878	−	0.145994i	0.925205	+	0.379467i	$0.123893\pi$
$710$		0			0
$711$	−32.1359	+	32.1359i	−1.20519	+	1.20519i
$712$		0			0
$713$	−4.03618	−	5.55532i	−0.151156	−	0.208048i
$714$		0			0
$715$	−10.1164	−	17.8195i	−0.378333	−	0.666410i
$716$		0			0
$717$	37.5653	−	27.2928i	1.40290	−	1.01927i
$718$		0			0
$719$	1.05966	−	6.69043i	0.0395186	−	0.249511i	−0.960018	−	0.279937i	$-0.909686\pi$
$719$	1.05966	−	6.69043i	0.0395186	−	0.249511i	0.999537	+	0.0304261i	$0.00968642\pi$
$720$		0			0
$721$	11.9849	+	23.5217i	0.446340	+	0.875992i
$722$		0			0
$723$	−1.08528	+	2.12998i	−0.0403619	+	0.0792147i
$724$		0			0
$725$	33.3682	−	40.0054i	1.23926	−	1.48576i
$726$		0			0
$727$	−16.5463	−	32.4739i	−0.613667	−	1.20439i	−0.963533	−	0.267590i	$-0.913773\pi$
$727$	−16.5463	−	32.4739i	−0.613667	−	1.20439i	0.349866	−	0.936800i	$-0.386227\pi$
$728$		0			0
$729$			40.6328i			1.50492i
$730$		0			0
$731$	28.3812	+	4.49515i	1.04972	+	0.166259i
$732$		0			0
$733$	10.8344	+	33.3447i	0.400176	+	1.23162i	0.924856	+	0.380316i	$0.124185\pi$
$733$	10.8344	+	33.3447i	0.400176	+	1.23162i	−0.524680	+	0.851299i	$0.675815\pi$
$734$		0			0
$735$	−6.87811	−	18.3141i	−0.253703	−	0.675524i
$736$		0			0
$737$		−	16.5708i		−	0.610394i
$738$		0			0
$739$	−3.48920			−0.128352			−0.0641762	−	0.997939i	$-0.520442\pi$
$739$	−3.48920			−0.128352			−0.0641762	+	0.997939i	$0.520442\pi$
$740$		0			0
$741$	−40.1783	−	40.1783i	−1.47599	−	1.47599i
$742$		0			0
$743$	−3.95950	−	12.1861i	−0.145260	−	0.447064i	0.851785	−	0.523892i	$-0.175521\pi$
$743$	−3.95950	−	12.1861i	−0.145260	−	0.447064i	−0.997044	+	0.0768286i	$0.975521\pi$
$744$		0			0
$745$	−10.6275	+	16.1080i	−0.389363	+	0.590150i
$746$		0			0
$747$	−89.1379			−3.26139
$748$		0			0
$749$	−22.1738	+	11.2981i	−0.810212	+	0.412823i
$750$		0			0
$751$	−5.83834	−	36.8618i	−0.213044	−	1.34511i	−0.829847	−	0.557990i	$-0.811573\pi$
$751$	−5.83834	−	36.8618i	−0.213044	−	1.34511i	0.616803	−	0.787117i	$-0.288427\pi$
$752$		0			0
$753$	31.6858	−	62.1868i	1.15469	−	2.26621i
$754$		0			0
$755$	−40.2947	+	1.81877i	−1.46648	+	0.0661920i
$756$		0			0
$757$	−41.6506	−	6.59681i	−1.51382	−	0.239765i	−0.656411	−	0.754404i	$-0.727926\pi$
$757$	−41.6506	−	6.59681i	−1.51382	−	0.239765i	−0.857407	+	0.514638i	$0.827926\pi$
$758$		0			0
$759$	11.7489	+	16.1710i	0.426458	+	0.586969i
$760$		0			0
$761$	41.5808	+	30.2102i	1.50730	+	1.09512i	0.967356	+	0.253423i	$0.0815563\pi$
$761$	41.5808	+	30.2102i	1.50730	+	1.09512i	0.539949	+	0.841698i	$0.318444\pi$
$762$		0			0
$763$	−9.11078	−	12.5399i	−0.329832	−	0.453975i
$764$		0			0
$765$	93.2042	−	35.0042i	3.36981	−	1.26558i
$766$		0			0
$767$	−25.9509	−	13.2226i	−0.937033	−	0.477442i
$768$		0			0
$769$	9.29877	−	28.6187i	0.335322	−	1.03202i	−0.631241	−	0.775587i	$-0.717454\pi$
$769$	9.29877	−	28.6187i	0.335322	−	1.03202i	0.966563	−	0.256429i	$-0.0825459\pi$
$770$		0			0
$771$	−8.64175	−	2.80788i	−0.311225	−	0.101123i
$772$		0			0
$773$	0.247425	+	1.56218i	0.00889926	+	0.0561877i	0.991738	−	0.128277i	$-0.0409448\pi$
$773$	0.247425	+	1.56218i	0.00889926	+	0.0561877i	−0.982839	+	0.184465i	$0.940945\pi$
$774$		0			0
$775$	−12.2067	+	20.4516i	−0.438478	+	0.734644i
$776$		0			0
$777$	−22.1241	−	16.0741i	−0.793699	−	0.576656i
$778$		0			0
$779$	−52.4117	−	5.17628i	−1.87784	−	0.185460i
$780$		0			0
$781$	1.58312	−	2.17897i	0.0566484	−	0.0779698i
$782$		0			0
$783$	−142.660	+	46.3532i	−5.09827	+	1.65653i
$784$		0			0
$785$	−29.4787	−	8.12843i	−1.05214	−	0.290116i
$786$		0			0
$787$	−4.39615	+	13.5300i	−0.156706	+	0.482291i	−0.998330	−	0.0577728i	$-0.981600\pi$
$787$	−4.39615	+	13.5300i	−0.156706	+	0.482291i	0.841624	+	0.540064i	$0.181600\pi$
$788$		0			0
$789$	−23.1066	+	71.1149i	−0.822617	+	2.53176i
$790$		0			0
$791$	−6.65863	+	13.0683i	−0.236754	+	0.464655i
$792$		0			0
$793$	0.672302	+	0.672302i	0.0238742	+	0.0238742i
$794$		0			0
$795$	5.51365	+	26.8976i	0.195549	+	0.953959i
$796$		0			0
$797$	8.67850	−	11.9449i	0.307408	−	0.423111i	−0.627162	−	0.778888i	$-0.715784\pi$
$797$	8.67850	−	11.9449i	0.307408	−	0.423111i	0.934571	+	0.355777i	$0.115784\pi$
$798$		0			0
$799$	−20.8673	−	28.7214i	−0.738232	−	1.01609i
$800$		0			0
$801$	12.5701	−	79.3648i	0.444144	−	2.80422i
$802$		0			0
$803$	16.3531	−	8.33232i	0.577088	−	0.294041i
$804$		0			0
$805$	5.22126	−	4.16575i	0.184025	−	0.146823i
$806$		0			0
$807$	64.1866	−	10.1662i	2.25947	−	0.357866i
$808$		0			0
$809$	3.77862	−	1.92531i	0.132849	−	0.0676901i	−0.386302	−	0.922372i	$-0.626248\pi$
$809$	3.77862	−	1.92531i	0.132849	−	0.0676901i	0.519152	+	0.854682i	$0.326248\pi$
$810$		0			0
$811$		−	22.4587i		−	0.788633i	−0.918975	−	0.394316i	$-0.870981\pi$
$811$		−	22.4587i		−	0.788633i	0.918975	−	0.394316i	$-0.129019\pi$
$812$		0			0
$813$	7.12181	−	44.9654i	0.249773	−	1.57700i
$814$		0			0
$815$	−11.0053	−	1.23748i	−0.385499	−	0.0433469i
$816$		0			0
$817$	27.9749	−	27.9749i	0.978718	−	0.978718i
$818$		0			0
$819$	32.9992			1.15309
$820$		0			0
$821$	−3.27105			−0.114160			−0.0570802	−	0.998370i	$-0.518179\pi$
$821$	−3.27105			−0.114160			−0.0570802	+	0.998370i	$0.518179\pi$
$822$		0			0
$823$	31.5012	−	31.5012i	1.09806	−	1.09806i	0.103425	−	0.994637i	$-0.467020\pi$
$823$	31.5012	−	31.5012i	1.09806	−	1.09806i	0.994637	−	0.103425i	$-0.0329801\pi$
$824$		0			0
$825$	35.5325	−	59.5326i	1.23708	−	2.07266i
$826$		0			0
$827$	−1.87420	+	11.8332i	−0.0651722	+	0.411481i	0.933436	+	0.358744i	$0.116795\pi$
$827$	−1.87420	+	11.8332i	−0.0651722	+	0.411481i	−0.998608	+	0.0527377i	$0.983205\pi$
$828$		0			0
$829$		−	46.3914i		−	1.61124i	−0.592432	−	0.805620i	$-0.701832\pi$
$829$		−	46.3914i		−	1.61124i	0.592432	−	0.805620i	$-0.298168\pi$
$830$		0			0
$831$	25.2675	−	12.8745i	0.876521	−	0.446610i
$832$		0			0
$833$	15.9670	−	2.52892i	0.553223	−	0.0876220i
$834$		0			0
$835$	24.2447	+	30.3878i	0.839024	+	1.05161i
$836$		0			0
$837$	61.1054	−	31.1347i	2.11211	−	1.07617i
$838$		0			0
$839$	2.04774	−	12.9289i	0.0706958	−	0.446356i	−0.926795	−	0.375567i	$-0.877448\pi$
$839$	2.04774	−	12.9289i	0.0706958	−	0.446356i	0.997491	−	0.0707894i	$-0.0225518\pi$
$840$		0			0
$841$	−46.7612	−	64.3612i	−1.61245	−	2.21935i
$842$		0			0
$843$	−21.9708	+	30.2402i	−0.756713	+	1.04153i
$844$		0			0
$845$	−3.78734	−	18.4760i	−0.130288	−	0.635594i
$846$		0			0
$847$	−10.8335	−	10.8335i	−0.372242	−	0.372242i
$848$		0			0
$849$	−24.2092	+	47.5133i	−0.830859	+	1.63065i
$850$		0			0
$851$	−1.81830	+	5.59616i	−0.0623306	+	0.191834i
$852$		0			0
$853$	−10.5242	+	32.3903i	−0.360343	+	1.10902i	0.592503	+	0.805568i	$0.298140\pi$
$853$	−10.5242	+	32.3903i	−0.360343	+	1.10902i	−0.952846	+	0.303454i	$0.901860\pi$
$854$		0			0
$855$	36.4372	−	132.144i	1.24613	−	4.51923i
$856$		0			0
$857$	−20.3005	+	6.59605i	−0.693453	+	0.225317i	−0.634476	−	0.772943i	$-0.718784\pi$
$857$	−20.3005	+	6.59605i	−0.693453	+	0.225317i	−0.0589775	+	0.998259i	$0.518784\pi$
$858$		0			0
$859$	−30.0079	+	41.3023i	−1.02386	+	1.40922i	−0.114392	+	0.993436i	$0.536492\pi$
$859$	−30.0079	+	41.3023i	−1.02386	+	1.40922i	−0.909464	+	0.415782i	$0.863508\pi$
$860$		0			0
$861$	33.1683	−	27.2056i	1.13037	−	0.927166i
$862$		0			0
$863$	−41.9354	−	30.4679i	−1.42750	−	1.03714i	−0.990476	−	0.137689i	$-0.956033\pi$
$863$	−41.9354	−	30.4679i	−1.42750	−	1.03714i	−0.437024	−	0.899450i	$-0.643967\pi$
$864$		0			0
$865$	−1.88474	+	16.7616i	−0.0640829	+	0.569911i
$866$		0			0
$867$	9.45271	+	59.6821i	0.321031	+	2.02691i
$868$		0			0
$869$	−24.8721	−	8.08145i	−0.843730	−	0.274144i
$870$		0			0
$871$	−2.55115	+	7.85164i	−0.0864425	+	0.266043i
$872$		0			0
$873$	2.57238	+	1.31069i	0.0870618	+	0.0443602i
$874$		0			0
$875$	−20.4089	−	10.9646i	−0.689947	−	0.370673i
$876$		0			0
$877$	25.3770	+	34.9285i	0.856922	+	1.17945i	0.982295	+	0.187342i	$0.0599872\pi$
$877$	25.3770	+	34.9285i	0.856922	+	1.17945i	−0.125373	+	0.992110i	$0.540013\pi$
$878$		0			0
$879$	−18.2338	−	13.2476i	−0.615010	−	0.446831i
$880$		0			0
$881$	4.84501	+	6.66858i	0.163232	+	0.224670i	0.882796	−	0.469756i	$-0.155658\pi$
$881$	4.84501	+	6.66858i	0.163232	+	0.224670i	−0.719564	+	0.694426i	$0.755658\pi$
$882$		0			0
$883$	38.5475	+	6.10532i	1.29723	+	0.205460i	0.766588	−	0.642139i	$-0.221953\pi$
$883$	38.5475	+	6.10532i	1.29723	+	0.205460i	0.530637	+	0.847599i	$0.321953\pi$
$884$		0			0
$885$	−4.44348	−	98.4448i	−0.149366	−	3.30918i
$886$		0			0
$887$	−18.2292	+	35.7768i	−0.612076	+	1.20127i	0.352090	+	0.935966i	$0.385471\pi$
$887$	−18.2292	+	35.7768i	−0.612076	+	1.20127i	−0.964166	+	0.265300i	$0.914529\pi$
$888$		0			0
$889$	3.56207	+	22.4900i	0.119468	+	0.754292i
$890$		0			0
$891$	−92.4307	+	47.0958i	−3.09654	+	1.57777i
$892$		0			0
$893$	−48.8787			−1.63566
$894$		0			0
$895$	2.56816	−	3.89251i	0.0858442	−	0.130112i
$896$		0			0
$897$	−3.07731	−	9.47098i	−0.102748	−	0.316227i
$898$		0			0
$899$	35.0942	+	35.0942i	1.17046	+	1.17046i
$900$		0			0
$901$	−22.6891			−0.755884
$902$		0			0
$903$			32.2248i			1.07237i
$904$		0			0
$905$	−17.8185	+	6.69200i	−0.592308	+	0.222450i
$906$		0			0
$907$	3.32161	+	10.2229i	0.110292	+	0.339444i	0.990936	−	0.134334i	$-0.0428896\pi$
$907$	3.32161	+	10.2229i	0.110292	+	0.339444i	−0.880644	+	0.473779i	$0.842890\pi$
$908$		0			0
$909$	−56.0586	−	8.87881i	−1.85935	−	0.294491i
$910$		0			0
$911$			7.54029i			0.249821i	0.992168	+	0.124910i	$0.0398644\pi$
$911$			7.54029i			0.249821i	−0.992168	+	0.124910i	$0.960136\pi$
$912$		0			0
$913$	−23.2869	−	45.7030i	−0.770683	−	1.51255i
$914$		0			0
$915$	−0.855122	+	3.10120i	−0.0282695	+	0.102523i
$916$		0			0
$917$	−0.326846	+	0.641472i	−0.0107934	+	0.0211833i
$918$		0			0
$919$	−9.52548	−	18.6948i	−0.314217	−	0.616685i	0.678845	−	0.734282i	$-0.262481\pi$
$919$	−9.52548	−	18.6948i	−0.314217	−	0.616685i	−0.993061	+	0.117597i	$0.962481\pi$
$920$		0			0
$921$	−4.94086	+	31.1953i	−0.162807	+	1.02792i
$922$		0			0
$923$	−1.08558	+	0.788720i	−0.0357323	+	0.0259610i
$924$		0			0
$925$	20.3263	−	1.83868i	0.668325	−	0.0604553i
$926$		0			0
$927$	55.8093	+	76.8149i	1.83302	+	2.52293i
$928$		0			0
$929$	−26.9178	+	26.9178i	−0.883144	+	0.883144i	−0.993853	−	0.110709i	$-0.964688\pi$
$929$	−26.9178	+	26.9178i	−0.883144	+	0.883144i	0.110709	+	0.993853i	$0.464688\pi$
$930$		0			0
$931$	10.1047	−	19.8315i	0.331167	−	0.649952i
$932$		0			0
$933$	−2.23212	−	0.725260i	−0.0730763	−	0.0237439i
$934$		0			0
$935$	42.2966	+	38.6432i	1.38325	+	1.26377i
$936$		0			0
$937$	3.83767	+	24.2301i	0.125371	+	0.791562i	0.967609	+	0.252455i	$0.0812381\pi$
$937$	3.83767	+	24.2301i	0.125371	+	0.791562i	−0.842237	+	0.539107i	$0.818762\pi$
$938$		0			0
$939$	11.5255	+	35.4718i	0.376120	+	1.15758i
$940$		0			0
$941$	−4.76834	+	6.56306i	−0.155444	+	0.213950i	−0.879635	−	0.475649i	$-0.842213\pi$
$941$	−4.76834	+	6.56306i	−0.155444	+	0.213950i	0.724192	+	0.689599i	$0.242213\pi$
$942$		0			0
$943$	−7.77262	−	4.97851i	−0.253111	−	0.162123i
$944$		0			0
$945$	32.9348	+	58.0125i	1.07137	+	1.88715i
$946$		0			0
$947$	−29.9023	+	9.71584i	−0.971694	+	0.315723i	−0.751500	−	0.659733i	$-0.770669\pi$
$947$	−29.9023	+	9.71584i	−0.971694	+	0.315723i	−0.220194	+	0.975456i	$0.570669\pi$
$948$		0			0
$949$	−9.03127	+	1.43041i	−0.293168	+	0.0464332i
$950$		0			0
$951$	0.509396	+	0.165513i	0.0165183	+	0.00536713i
$952$		0			0
$953$	−10.5902	−	3.44098i	−0.343051	−	0.111464i	0.132424	−	0.991193i	$-0.457724\pi$
$953$	−10.5902	−	3.44098i	−0.343051	−	0.111464i	−0.475475	+	0.879729i	$0.657724\pi$
$954$		0			0
$955$	3.38497	+	4.24265i	0.109535	+	0.137289i
$956$		0			0
$957$	−102.156	−	102.156i	−3.30222	−	3.30222i
$958$		0			0
$959$	27.1854	−	19.7513i	0.877861	−	0.637804i
$960$		0			0
$961$	6.72219	+	4.88396i	0.216845	+	0.157547i
$962$		0			0
$963$	−72.4131	+	52.6112i	−2.33348	+	1.69537i
$964$		0			0
$965$	0.212148	−	0.321549i	0.00682929	−	0.0103510i
$966$		0			0
$967$	20.4762	−	10.4331i	0.658469	−	0.335507i	−0.0926256	−	0.995701i	$-0.529526\pi$
$967$	20.4762	−	10.4331i	0.658469	−	0.335507i	0.751095	+	0.660194i	$0.229526\pi$
$968$		0			0
$969$	141.552	+	72.1245i	4.54732	+	2.31697i
$970$		0			0
$971$	−0.788409	−	4.97782i	−0.0253012	−	0.159746i	0.971803	−	0.235795i	$-0.0757694\pi$
$971$	−0.788409	−	4.97782i	−0.0253012	−	0.159746i	−0.997104	+	0.0760493i	$0.975769\pi$
$972$		0			0
$973$	−8.62916	−	16.9357i	−0.276638	−	0.542933i
$974$		0			0
$975$	−26.0014	+	22.7375i	−0.832712	+	0.728184i
$976$		0			0
$977$	−6.24192	+	39.4099i	−0.199697	+	1.26084i	0.660482	+	0.750842i	$0.270352\pi$
$977$	−6.24192	+	39.4099i	−0.199697	+	1.26084i	−0.860179	+	0.509993i	$0.829648\pi$
$978$		0			0
$979$	43.9760	−	14.2887i	1.40548	−	0.456668i
$980$		0			0
$981$	−39.4206	−	39.4206i	−1.25860	−	1.25860i
$982$		0			0
$983$		−	4.22330i		−	0.134702i	−0.997729	−	0.0673512i	$-0.978545\pi$
$983$		−	4.22330i		−	0.134702i	0.997729	−	0.0673512i	$-0.0214548\pi$
$984$		0			0
$985$	39.7671	+	18.0522i	1.26708	+	0.575191i
$986$		0			0
$987$	28.1521	−	28.1521i	0.896091	−	0.896091i
$988$		0			0
$989$	6.59434	−	2.14263i	0.209688	−	0.0681317i
$990$		0			0
$991$	−24.0685	−	3.81208i	−0.764561	−	0.121095i	−0.238039	−	0.971256i	$-0.576504\pi$
$991$	−24.0685	−	3.81208i	−0.764561	−	0.121095i	−0.526523	+	0.850161i	$0.676504\pi$
$992$		0			0
$993$	−8.75182			−0.277731
$994$		0			0
$995$	1.89131	+	41.9018i	0.0599587	+	1.32838i
$996$		0			0
$997$	4.52762	−	0.717104i	0.143391	−	0.0227109i	−0.0843263	−	0.996438i	$-0.526874\pi$
$997$	4.52762	−	0.717104i	0.143391	−	0.0227109i	0.227717	+	0.973727i	$0.426874\pi$
$998$		0			0
$999$	−52.3615	−	26.6795i	−1.65664	−	0.844102i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bq.a.49.1	✓	176
5.4	even	2	inner	820.2.bq.a.49.22	yes	176
41.36	even	20	inner	820.2.bq.a.569.22	yes	176
205.159	even	20	inner	820.2.bq.a.569.1	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bq.a.49.1	✓	176	1.1	even	1	trivial
820.2.bq.a.49.22	yes	176	5.4	even	2	inner
820.2.bq.a.569.1	yes	176	205.159	even	20	inner
820.2.bq.a.569.22	yes	176	41.36	even	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.bq (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.28615 + 2.28615i) q^{3} +(-0.249857 + 2.22206i) q^{5} +(0.324162 - 2.04668i) q^{7} -7.45299i q^{9} +(3.82132 - 1.94706i) q^{11} +(-2.11039 + 0.334253i) q^{13} +(-4.50877 - 5.65119i) q^{15} +(5.32295 - 2.71218i) q^{17} +(1.28670 - 8.12389i) q^{19} +(3.93794 + 5.42011i) q^{21} +(0.847314 - 1.16623i) q^{23} +(-4.87514 - 1.11040i) q^{25} +(10.1802 + 10.1802i) q^{27} +(-4.73011 + 9.28337i) q^{29} +(1.47200 - 4.53036i) q^{31} +(-4.28485 + 13.1874i) q^{33} +(4.46686 + 1.23169i) q^{35} +(-3.88208 + 1.26136i) q^{37} +(4.06052 - 5.58883i) q^{39} +(-0.375244 - 6.39212i) q^{41} +(3.89132 + 2.82721i) q^{43} +(16.5610 + 1.86219i) q^{45} +(-0.929626 - 5.86942i) q^{47} +(2.57358 + 0.836207i) q^{49} +(-5.96863 + 18.3695i) q^{51} +(-3.38397 - 1.72422i) q^{53} +(3.37171 + 8.97771i) q^{55} +(15.6309 + 21.5140i) q^{57} +(11.0277 + 8.01213i) q^{59} +(-0.261551 - 0.359994i) q^{61} +(-15.2539 - 2.41598i) q^{63} +(-0.215435 - 4.77294i) q^{65} +(1.75412 - 3.44265i) q^{67} +(0.729086 + 4.60326i) q^{69} +(0.559555 - 0.285107i) q^{71} +4.27944 q^{73} +(13.6839 - 8.60678i) q^{75} +(-2.74628 - 8.45218i) q^{77} +(-4.31181 - 4.31181i) q^{79} -24.1881 q^{81} -11.9600i q^{83} +(4.69666 + 12.5056i) q^{85} +(-10.4094 - 32.0370i) q^{87} +(10.6487 + 1.68659i) q^{89} +4.42764i q^{91} +(6.99187 + 13.7223i) q^{93} +(17.7303 + 4.88894i) q^{95} +(-0.175861 + 0.345147i) q^{97} +(-14.5114 - 28.4803i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 4 q^{11} - 10 q^{15} - 4 q^{19} + 12 q^{25} + 8 q^{29} - 8 q^{31} - 6 q^{35} + 40 q^{39} + 28 q^{41} - 4 q^{45} + 20 q^{49} - 32 q^{51} - 50 q^{55} + 12 q^{59} + 40 q^{61} - 10 q^{65} - 28 q^{69}+ \cdots + 4 q^{99}+O(q^{100}) \) 176 * q + 4 * q^11 - 10 * q^15 - 4 * q^19 + 12 * q^25 + 8 * q^29 - 8 * q^31 - 6 * q^35 + 40 * q^39 + 28 * q^41 - 4 * q^45 + 20 * q^49 - 32 * q^51 - 50 * q^55 + 12 * q^59 + 40 * q^61 - 10 * q^65 - 28 * q^69 - 108 * q^71 + 52 * q^75 + 48 * q^79 - 328 * q^81 + 98 * q^85 - 16 * q^89 + 26 * q^95 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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